Code search problems refer to searching a particular bit pattern that satisfies given constraints. Obtaining such codes is very important in fields such as data encoding, error correcting, cryptography, etc. Unfortunately, the search time increases exponentially with the number of bits in the code, and typically requires many months of computation to find large codes. On the other hand, the search method mostly consists of 1-bit computations, so that reconfigurable hardware such as FPGAs (field programmable gate arrays) can be used to successfully obtain a massive degree of parallelism. In this paper, we propose a heterogeneous system with a CPU and an FPGA to speed-up code search problems. According to the evaluation, we obtain over 86 times speed-up compared to typical CPU-based implementation for extremal doubly even self-dual code search problem of length 128.